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論文名稱 Title |
極化碼的有效解碼演算法研究 A Study of Efficient Decoding Algorithms for Polar Codes |
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系所名稱 Department |
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畢業學年期 Year, semester |
語文別 Language |
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學位類別 Degree |
頁數 Number of pages |
81 |
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研究生 Author |
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指導教授 Advisor |
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召集委員 Convenor |
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口試委員 Advisory Committee |
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口試日期 Date of Exam |
2018-07-31 |
繳交日期 Date of Submission |
2018-08-27 |
關鍵字 Keywords |
通道極化、極化碼、極化碼建構、極化碼解碼、Shannon極限 Channel polarization, polar code, polar code construction, polar code decoding, Shannon limit |
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統計 Statistics |
本論文已被瀏覽 5645 次,被下載 7 次 The thesis/dissertation has been browsed 5645 times, has been downloaded 7 times. |
中文摘要 |
極化碼(Polar Code)是在2009年由E. Arikan提出的一種新的錯誤更正碼,是依據通道極化(Channel Polarization)現象,有些通道的通道容量(Channel Capacity)會趨近於1,有些通道的通道容量則會趨於0的這個特性來設計編碼與解碼,並且已經被證明可在任何二位元離散無記憶性通道(Binary Discrete Memoryless Channel)中達到Shannon極限。 一開始,我們在本論文中介紹極化碼的基礎知識,包含通道合併(Channel Combining)、通道分裂(Channel Spiliting)以及如何編碼(Encode)。並針對極化碼建構方法進行了研究,考慮了四種不同的方法:巴氏參數(Bhattacharyya Parameter)法、列權重(Row Weight)法、高斯近似(Gaussian Approximation)法以及極化權重(Polarization Weight)法,說明了他們各有甚麼優缺點。 其次,連續消除(Successive Cancellation)解碼是最先被提出的極化碼解碼方法,但在碼長較短的情況下,效能會大幅的下降。所以置信傳播(Belief Propagation)解碼,列表連續消除(Successive Cancellation List)解碼,軟消除(Soft Cancellation)解碼和連續消除反轉(Successive Cancellation Flip, SC-Flip)解碼相繼被提出,我們針對這些解碼去分析和比較其效能和複雜度的差異。 最後,我們根據SC-Flip解碼,提出一個改進的SC-Flip解碼,透過分段解碼和根據觀察錯誤通道雜訊引起的位置從中挑出比較重要的位置進行反轉就好。可以比原本的SC-Flip解碼效能要好,運算複雜度也可以降低,從而有更好的吞吐量(Throughput)。 |
Abstract |
Polar code is a new type of error-correcting code proposed by E. Arikan in 2009. It is based on channel polarization. The channel capacity of some sub-channels approaches 1; however, others approach 0. And it is proven that the capacity can achieve Shannon limit in any binary-discrete memoryless channel. At first, we introduce the fundamental knowledge of polar code in the present study, including channel combining, channel splitting, and how to encode. We carry out a research in polar code construction method, taking four different methods with the pros and cons explained into consideration: Bhattacharyya parameter, row weight, Gaussian approximation, and polarization weight. What’s more, successive cancellation is the very first polar code decoding method. With shorter codeword length, the performance will decrease significantly. So decoding methods like belief propagation, successive cancellation List, soft cancellation, and successive cancellation flip(SC-Flip) are proposed. We focus on these decoding methods, analyzing and comparing the differences between performance and complexity. Based on SC-Flip, we bring up an enhanced SC-Flip. Through segment decoding and observing the indices are wrong caused by channel noise, among which we choose a more important one to flip. By doing so, the performance goes up; in the meanwhile, the computing complexity goes down, which therefore leads to better throughput. |
目次 Table of Contents |
論文審定書 i 誌謝 ii 中文摘要 iii ABSTRACT iv 目錄 v 圖次 viii 表次 x Chapter 1 導論 1 1.1 研究背景 2 1.2 研究動機 4 1.3 論文架構 4 Chapter 2 極化碼基礎與編碼 6 2.1 通道容量 6 2.2 通道極化 7 2.2.1 通道合併 7 2.2.2 通道分裂 10 2.2.3 極化效應 11 2.3 極化碼編碼 14 Chapter 3 極化碼的建構方法 16 3.1 列權重法 16 3.2 Bhattacharyya參數法 17 3.3 高斯近似法 17 3.4 極化權重法 18 Chapter 4 極化碼數種解碼方法 20 4.1 連續刪除解碼 20 4.2 列表連續消除解碼 25 4.2.1 CRC列表連續消除解碼 30 4.3 置信傳播解碼 30 4.4 軟消除解碼 34 4.4.1 LDPC結合SCAN解碼 35 Chapter 5 連續消除反轉解碼及其改進 38 5.1 連續消除反轉解碼 38 5.2 改進的連續消除反轉解法 43 5.2.1 通道雜訊引起的錯誤位置選擇 43 5.2.2 分段斷點位置選擇 44 5.2.3 改進的連續消除反轉解法的演算法 46 Chapter 6 模擬結果 48 6.1 不同碼長的極化碼效能比較 48 6.2 不同建構方法的極化碼效能比較 50 6.3 第四章解碼方法的極化碼效能比較 52 6.3.1 不同L大小的SCL解碼效能比較 52 6.3.2 CRC對SCL的影響 52 6.3.3 軟判決解碼的效能比較 53 6.4 改進的SC-Flip解碼與其他解碼比較 55 6.4.1 改進的SC-Flip解碼與SC-Flip解碼比較 55 6.4.2 不同解碼方法的比較 56 Chapter 7 結論 59 REFERENCES 60 中英對照表 65 縮寫對照表 69 |
參考文獻 References |
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